Question: Simplify the following expression and state the condition under which the simplification is valid. $k = \dfrac{p^2 - 4}{p + 2}$
Explanation: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = p$ $ b = \sqrt{4} = 2$ So we can rewrite the expression as: $k = \dfrac{({p} + {2})({p} {-2})} {p + 2} $ We can divide the numerator and denominator by $(p + 2)$ on condition that $p \neq -2$ Therefore $k = p - 2; p \neq -2$